Re: My mostly hard sci-fi campaign
A few notes on some of your proposed colonies.
Given that Mercury's day is ~2/3 its year, a synchronous orbit would be so far away that Sol would have an overwhelmingly more powerful gravitational attraction. In short, your colony would land up orbiting Sol, not Mercury.
As above, only more so, as Venus rotates retrograde.
Two points:
1) Are you talking about Earth-Luna Lagrange points, or Sol-Earth Lagrange points?
2) Only L4 and L5 points are usefully stable: L1, L2, and L3 are stable only in the theoretical situation where (A) the second body's orbit is utterly circular and ( there are only three bodies in the universe. With Luna's orbit not being a perfect circle and with other bodies (particularly Sol) pulling on anything in the first 3 Lagrange points, such stations would need to expend a boatload of propellant staying "on station".
I suggest you double check; as far as I can find out, Chryse Planitia is not on Mars's equator.
Unless your setting has ships with enough power and enough propellant capacity to not use Hohmann orbits, they'll be there a whole lot longer.
Not possible; synchronous orbits have to have an average "latitude" of the equator. You can have one that goes as far south as the Red Spot, but it will go as far north, as well.
See last.
That "chaotic" rotation will make landing and take-off ludicrously difficult, if possible at all. And its mass is high enough that "regularizing" the rotation is impractical.
I don't have enough information to be sure, but my gut feeling is a synchronous orbit will be inside the rings.
BTW, "geosynchronous" is only used WRT Earth. "Synchronous" can be applied to any body, without having to figure out the proper Greek-/Latin-derived term.
See last.